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978-3-8439-4072-6, Reihe Mathematik

Kathinka Hameister A dual tailored branch-and-bound algorithm for quadratic mixed-integer problems Applied to production models with buffers

220 Seiten, Dissertation Universität Mannheim (2018), Softcover, A5

Using tools of the mathematical modeling, we are able to reproduce complex interrelationships and simulate or optimize the underlying dynamics with a computing system. Examples can be taken from the simulation of traffic flows on roads, water flows in pipes or the flows of products within a production environment or in the context of global logistics. The computed data is often used for forecasts or diagnoses on a running system. There is an increasing interest in controlling these flows e.g., in the context of a traffic flow via traffic lights or speed limits. Considering a production environment, we can find a control on the production flow in the distribution of the employees who need to operate the production lines.

Many of the above mentioned applications of mathematical optimization can be represented as a mixed integer quadratic constraint quadratic problem. Therefore, we present an improved solution method based on the branch-and-bound algorithm for this general problem class in the beginning of this thesis.

In the second part, we will focus on the optimization of decision variables in the context of a semi-automatic operating production system which will be modeled as a network. To model the present dynamics, we consider partial differential equations coupled by ordinary differential equations. With the ambition to optimize this discrete-continuous optimization problem, we fully discretize the model with linear numerical methods. In this way, we are able to stay within the context of mixed-integer quadratic constraint quadratic problems. To obtain additional information for the optimization process as well as for the calculation of dual bound, we derive the adjoint system. This provides the opportunity to equip the branch-and-bound algorithm with knowledge about the structure of the discretized optimization problem. Furthermore, heuristics are presented which reliably provide sufficiently good starting solutions for solving these special optimization problems.